Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-36f^2g^3\frac{h^4}{42}f^3g^7h^7& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{36f^2g^3h^4}{42}f^3g^7h^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36f^5g^3h^4}{42}g^7h^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{36f^5g^{10}h^4}{42}h^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{36f^5g^{10}h^{11}}{42}\end{aligned} $$ | |
| ① | Multiply $36f^2g^3$ by $ \dfrac{h^4}{42} $ to get $ \dfrac{ 36f^2g^3h^4 }{ 42 } $. Step 1: Write $ 36f^2g^3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 36f^2g^3 \cdot \frac{h^4}{42} & \xlongequal{\text{Step 1}} \frac{36f^2g^3}{\color{red}{1}} \cdot \frac{h^4}{42} \xlongequal{\text{Step 2}} \frac{ 36f^2g^3 \cdot h^4 }{ 1 \cdot 42 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36f^2g^3h^4 }{ 42 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{36f^2g^3h^4}{42} $ by $ f^3 $ to get $ \dfrac{ 36f^5g^3h^4 }{ 42 } $. Step 1: Write $ f^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{36f^2g^3h^4}{42} \cdot f^3 & \xlongequal{\text{Step 1}} \frac{36f^2g^3h^4}{42} \cdot \frac{f^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 36f^2g^3h^4 \cdot f^3 }{ 42 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36f^5g^3h^4 }{ 42 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{36f^5g^3h^4}{42} $ by $ g^7 $ to get $ \dfrac{ 36f^5g^{10}h^4 }{ 42 } $. Step 1: Write $ g^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{36f^5g^3h^4}{42} \cdot g^7 & \xlongequal{\text{Step 1}} \frac{36f^5g^3h^4}{42} \cdot \frac{g^7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 36f^5g^3h^4 \cdot g^7 }{ 42 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36f^5g^{10}h^4 }{ 42 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{36f^5g^{10}h^4}{42} $ by $ h^7 $ to get $ \dfrac{ 36f^5g^{10}h^{11} }{ 42 } $. Step 1: Write $ h^7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{36f^5g^{10}h^4}{42} \cdot h^7 & \xlongequal{\text{Step 1}} \frac{36f^5g^{10}h^4}{42} \cdot \frac{h^7}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 36f^5g^{10}h^4 \cdot h^7 }{ 42 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36f^5g^{10}h^{11} }{ 42 } \end{aligned} $$ |